We are with sleep-talkers, a less-often encountered term than sleep-walkers, even though the former are more common. Medical terminology has dignified words for them both: somnambulants and somniloquents. Some sufferers have been known to do both at once: you might call this the Lady Macbeth syndrome.
Both words begin with a derivative of the Latin somnus, sleep. The second parts are respectively from ambulare, to walk, and loqui, to speak. The former verb appears in perambulate, to walk about in a leisurely way, and in ambulant, a patient who is not confined to bed but is able to walk about. The rather rare noctambulant, somebody who walks at night, is from the same source; he or she might be somnambulant but could equally be insomniac. As to the second, if you talk a lot while awake, you are better described by its relative loquacious.
The nouns belonging to them are somnambulism and somniloquy. (Though most somniloquies are also soliloquies, it’s best not to confuse the two.) Somniloquacious is a pleasant adjectival expansion which trips off the tongue. Nathan Bailey included it in his dictionary in 1731 with the same sense as somnliloquent. It hasn’t been encountered in the wild since, though a music magazine did feature somniloquaciously some decades ago.